Method and a Device to Compensate for Imbalances in a Receiver

ABSTRACT

The invention concerns a method for the correction of the IQ imbalance of a receiver, in order to obtain a corrected estimate of the IQ imbalance, including: a step for estimating IQ imbalance according to imbalance residual variations since a preceding estimate of the IQ imbalance, a step correcting frequency and clock offsets, a step for correcting the IQ imbalance according to the estimate of the imbalance, in order to obtain a corrected estimate of the IQ imbalance.

TECHNICAL FIELD AND PRIOR ART

The invention concerns the field of signal processing.

It applies to radio receivers in general.

It concerns in particular frequency and clock synchronisation andchannel estimate of multi-carrier reception systems, in the presence ofimbalances of gain and phase between the paths in phase and in phasequadrature.

FIG. 1A represents a transmitter (emitter) 2, that includes signalgenerating means 4, frequency transposition means 6, filtration means 8,12, amplification means 10, and an antenna 14.

FIG. 1B represents a receiver 20, that includes an antenna 21,filtration means 22, 24, and amplification means 23. Reference 25indicates a local oscillator, references 26 and 28 are mixers,respectively followed by filters 27, 29, and all of these means 25 to 29form frequency transposition means. An analogue signal processed bythese means is then digitised by digitising means 30 and digitalprocessing means 32, to produce a signal 34.

Many wireless communication systems now convey or will conveyinformation on several orthogonal subcarriers.

This is the case of the systems called OFDM and MC-CDMA, which offer agood strength to multipath propagation channels, and to selectivefading.

The receivers that use this orthogonal frequency multiplexing no longerfunction correctly when there is a frequency or clock offset between thetransmitter and the receiver.

These systems are also sensitive to imbalances of gain and phase betweenthe paths in phase and phase quadrature in the receiver. Thesuperimposition of these distorting elements generates inter-carrierinterference and renders demodulation particularly difficult.

It is possible to evaluate the degradations undergone byfrequency-defined sequences (pilots or “learning sequences”) at thetransmission step in multicarrier systems.

We begin by calculating the effect of the frequency and clock offset atthe FFT output.

Let [X_(−K), . . . , X⁻¹, X₁, . . . , X_(K)] be the coded signal to betransmitted on the 2K OFDM subcarriers.

At transmission, the temporal signal at the IFFT output is given by:$x_{n} = {\frac{1}{2\quad K}{\sum\limits_{k = {- K}}^{K}{X_{k}{\mathbb{e}}^{j*2\quad\pi*\frac{k*n}{2\quad K}}}}}$

At the output of the gaussian channel, and after transposition tobaseband, the signal affected by the frequency offset Δf and clockoffset δt, becomes:$y_{n} = {{\frac{1}{2\quad K}{\sum\limits_{k = {- K}}^{K}{X_{k}H_{k}{\mathbb{e}}^{j*2\quad{\pi{({k + {\Delta\quad f\quad T}})}}\frac{{({1 + {\frac{\delta}{T}t}})}n}{2\quad K}}}}} + w_{n}}$

where T is the symbol period, with coefficients H_(k) beingrepresentative of the propagation channel, and where w_(n) refers toadded noise.

After passage in the FFT step (Fast Fourier Transform), we get:$Y_{p} = {{\frac{1}{2\quad K}{\sum\limits_{n = {- K}}^{K}{\sum\limits_{k = {- K}}^{K}{X_{k}H_{k}{\mathbb{e}}^{j*2\quad\pi\frac{{{({k + {\Delta\quad f\quad T}})}{({1 + \frac{\delta\quad t}{T}})}} - p}{2\quad K}n}}}}} + W_{p}}$

where W_(p) refers to added noise.

It is possible to make the following simplifying assumptions: Δf.δt<<δt

Making the substitution and expanding we get:$Y_{p} = {{X_{p}H_{p}\frac{\sin\quad\left( {\pi\left( {{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}} \right)} \right)}{2\quad K\quad{\sin\left( \frac{\pi\left( {{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}} \right)}{2\quad K} \right)}}{\mathbb{e}}^{j*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}{({{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}})}}} + {\sum\limits_{\underset{k \neq p}{k = {- K}}}^{K}{X_{k}H_{k}\quad\frac{\sin\left( {\pi\left( {k - p + {\Delta\quad f\quad T} + {k\quad\frac{\delta\quad t}{T}}} \right)} \right)}{2\quad K\quad{\sin\left( \frac{\pi\left( {k - p + {\Delta\quad f\quad T} + {k\quad\frac{\delta\quad t}{T}}} \right)}{2\quad K} \right)}}{\mathbb{e}}^{j*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}{({k - p + {\Delta\quad f\quad T} + {k\quad\frac{\delta\quad t}{T}}})}}}} + W_{p}}$

The signal, thus affected by a frequency and clock offset experiences aphase shift, a change in gain, and the appearance of inter-carrierinterference.

In the presence of IQ imbalances, the inter-carrier interference isfurther accentuated. We can model the composition of these imperfectionsby a block of frequency and clock offsets followed by a block of IQimbalances. At the FFT output, the expression becomes:$Y_{p} = {{\left( {{{\alpha \cdot X_{p}}H_{p}{\mathbb{e}}^{j\quad*2\quad\pi*\frac{{2K} - 1}{2\quad K}{({{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}})}}} + {{\beta \cdot X_{p}^{*m}}H_{p}^{*m}{\mathbb{e}}^{{- j}\quad*2\quad\pi*\frac{{2K} - 1}{2\quad K}{({{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}})}}}} \right)\frac{\sin\left( {\pi\left( {{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}} \right)} \right)}{2\quad K\quad{\sin\left( \frac{\pi\left( {{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}} \right)}{2\quad K} \right)}}} + {\alpha{\sum\limits_{\underset{k \neq p}{k = {- K}}}^{K}{X_{k}H_{k}\quad\frac{\sin\left( {\pi\left( {k - p + {\Delta\quad f\quad T} + \frac{\delta\quad t}{T}} \right)} \right)}{2\quad K\quad{\sin\left( {\pi\frac{k - p + {\Delta\quad f\quad T} + \frac{\delta\quad t}{T}}{2\quad K}} \right)}}{\mathbb{e}}^{j*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}{({k - p + {\Delta\quad f\quad T} + \frac{\delta\quad t}{T}})}}}}} + {\beta{\sum\limits_{\underset{k \neq p}{k = {- K}}}^{K}{X_{k}^{*m}H_{k}^{*m}\quad\frac{\sin\left( {\pi\left( {k - p + {\Delta\quad f\quad T} + \frac{\delta\quad t}{T}} \right)} \right)}{2\quad K\quad{\sin\left( {\pi\frac{k - p + {\Delta\quad f\quad T} + \frac{\delta\quad t}{T}}{2\quad K}} \right)}}{\mathbb{e}}^{{- j}*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}{({k - p + {\Delta\quad f\quad T} + \frac{\delta\quad t}{T}})}}}}} + W_{2\quad p}}$

where *m refers to the conjugate mirror subcarrier, and where α and βate the parameters of the IQ imbalances.

When such distorting elements are superimposed, the channel estimate andequalisation algorithms are biased, and the IQ imbalances estimate andcompensation systems are damaged.

FIGS. 2A and 2B represent diagrams of compensation devices as describedin document WO03/101064.

In this document, an IQ imbalance correction and a frequency offsetcorrection are carried out jointly from continuous-frequency OFDMpilots. The principle of the IQ imbalances correction is based upon achannel estimate frequency “smoothing”.

According to the estimated frequency offset, the IQ imbalancesevaluation is carried out by an algorithm in the frequency domain(IQ-FD) or the time domain (IQ-TD) and compensated at a later step, asillustrated respectively in FIGS. 3 and 5 of this document.

This switching from one algorithm to the other allows one to reduce thecomplexity of the calculations by dispensing with the interference termsbetween subcarriers.

The implantation of these two algorithms, and their switching, iscomplex to implement however. For a hardware system, two circuits arenecessary, and this occupies space on a chip. For a software system, twoprograms are necessary, occupying space in memory.

In addition, data compensation requires one to be in possession ofestimates of the frequency offset and of the IQ imbalances, afterprocessing the learning sequences (including FFT). This can give rise toa latency period during which the data are waiting for these estimates.

Moreover, channel estimate needs to be corrected according to theseestimates, and this increases the complexity.

It is possible finally to criticise this algorithm on the grounds of alack of flexibility: it is necessary to have two learning sequences insuccession in order to effect the frequency offset estimate, and of theIQ imbalances in the case of a large frequency offset (the IQ-TDalgorithm). These long consecutive learning sequences are not alwaysavailable in the current telecommunication standards.

This therefore raises the problem of finding a method to measure orestimate the IQ imbalances in the presence of a frequency offset betweenthe transmitter and receiver, which does not have the limitations of theprior art described above.

PRESENTATION OF THE INVENTION

This present invention allows one to remedy these drawbacks.

The invention concerns a method for correction of the IQ imbalancesestimate of a receiver, called the preceding estimate, in order toobtain a corrected IQ imbalance, in which the correction is carried outaccording to the imbalance residual variations since said precedingestimate.

According to the invention, we effect:

an estimate of the correction of the IQ imbalance estimate, according toimbalance residual variations,

a correction of the frequency and/or clock offsets, and of the IQimbalance, according to the estimate of the imbalance, in order toobtain a corrected IQ imbalance or a corrected estimate of the IQimbalance.

The method according to the invention requires no placing in memory ofsignals, and generates no latency period.

The IQ imbalances estimate is conducted by means of an adaptivealgorithm, from a new criterion that is not very sensitive to thefrequency offsets.

This offers a robust solution, as well as flexibility in use. Only onealgorithm is necessary, whatever the frequency domain. It also functionsfrom pilots or from learning sequences that are not necessarilyconsecutive.

Finally, channel estimate soon needs no further correction: thecorrection takes place upstream of the fast Fourier transform operation,or during this operation, but not directly on the channel estimatingoperation.

On the contrary, the processes described in document WO03/101064 firstlydraw the imbalance estimate parameters from the channel estimate, andsecondly also require a channel estimate correction.

IQ imbalances compensation can be carried out from continuous frequencypilots that are not necessarily consecutive.

The IQ imbalance estimate can be carried out from pilots, or learningsequences, which give rise to transitions due to the opposite IQimbalances.

Thus, with such pilots, given that the interference generated by an IQimbalance can be added to or subtracted from the complex received signalaccording to the sign of the ratio between the transmitted OFDM symboland its mirror part, with the transitions due to the IQ imbalances beingopposite, the IQ imbalances correction is improved.

The IQ imbalance estimate can be carried out from two pilots, orlearning sequences.

The IQ imbalance estimate can be carried out, for example, from twopilots or learning sequences, p₁ and p₂, with p₁, being composed of apseudo-random sequence for example, and p₂ being identical to p₁ forexample, in the first half of its samples and opposite to p₁ in thesecond half of its samples.

With these two pilots, we get transitions due to the IQ imbalances whichare opposite.

The imbalance residual variations can be calculated according to aninterference signal of mirror carriers and subcarriers, according to acriterion for minimising the envelope of the interference signal forexample.

A parameter |E|², which is characteristic of the envelope of saidinterference signal, can be used for this purpose.

Preferably, only the transitions of the interference signal are takeninto account.

According to one embodiment:

we measure the value of the complex frequency samples of pilots receivedin the neighbourhood of the transitions,

we compare these samples to the samples of the transmitted pilot, andfrom these we extract the characteristic parameter |E|² of the envelopeof the IQ imbalances interference.

Parameter |E|² can, for example, be equal or proportional to:${{E(n)}}^{2} = {\frac{\left( {{{S_{5}(n)}{p\left( {n + 1} \right)}} - {{S_{5}\left( {n + 1} \right)}{p(n)}}} \right){p_{m}(n)}}{\left( {{{p\left( {n + 1} \right)}{p_{m}(n)}} - {{p(n)}{p_{m}\left( {n + 1} \right)}}} \right){S_{5}(n)}^{m^{*}}}}^{2}$and  thus: ${{E(n)}}^{2} = {\frac{\begin{matrix}{{\left( {{{S_{5}(n)}{p\left( {n + 1} \right)}} - {{S_{5}\left( {n + 1} \right)}{p(n)}}} \right){p_{m}(n)}} -} \\{\left( {{{S_{5}\left( {n + 1} \right)}{p\left( {n + 2} \right)}} - {{S_{5}\left( {n + 2} \right)}{p\left( {n + 1} \right)}}} \right){p_{m}\left( {n + 1} \right)}}\end{matrix}}{\begin{matrix}{{{S_{5}(n)}^{m^{*}}\left( {{{p\left( {n + 1} \right)}{p_{m}(n)}} - {{p(n)}{p_{m}\left( {n + 1} \right)}}} \right)} -} \\{{S_{5\quad m}\left( {n + 1} \right)}^{*}\left( {{{p\left( {n + 2} \right)}{p_{m}\left( {n + 1} \right)}} - {{p\left( {n + 1} \right)}{p_{m}\left( {n + 2} \right)}}} \right)}\end{matrix}}}^{2}$

where S₅(n) is the received signal on subcarrier “n”, S_(5m)(n) is thereceived signal on the mirror subcarrier, p(n) is the value of the piloton subcarrier “n” and p_(m)(n) is the pilot on the mirror subcarrier.

The βest estimate of the IQ imbalances can be corrected, in relation tothe preceding estimate, proportionally to$\frac{\partial{E}^{2}}{\partial\beta^{\prime}},$where β′ represents the residual IQ imbalance.

The invention also concerns a method for correction of the IQ imbalanceof a receiver, in the presence of a frequency and/or clock offset, inorder to obtain a corrected estimate of the IQ imbalance. According tothe invention, we perform:

an IQ imbalance estimate carried out from pilots, or learning sequences,which give rise to transitions due to the IQ imbalances which areopposite,

a correction of the frequency and/or clock offsets and of the IQimbalance according to the estimate of the imbalance, in order to obtaina corrected estimate of the IQ imbalance.

The pilots employed in this method are used to obtain transitions due tothe IQ imbalances which are opposite.

The IQ imbalances estimate is conducted using an algorithm which here isnot necessarily adaptive, by virtue of the opposite transitionsobtained, the compensation of the IQ imbalance and of any frequencyoffset can then be carried out directly, without the use of imbalanceresidual variations.

The IQ imbalance estimate can be carried out from two pilots or learningsequences.

The IQ imbalance estimate can, for example, be carried out from twopilots or learning sequences, p₁ and p₂, where p₁ is composed of apseudo-random sequence and p₂ is identical to p₁ in the first half ofits samples and opposite to p₁ in the second half of its samples.

The invention also concerns a method for the correction of a signal s2received and digitised by a wireless receiver, including a correction ofthe IQ imbalance as presented above, and correction of the signal s2according to this imbalance.

The correction of signal s2 is preferably carried out before a Fouriertransform operation.

The imbalance residual variations can be obtained from the signal S4obtained by fast Fourier transform (FFT) in the receiver.

According to the invention, compensation of the frequency and clockoffsets as well as of the IQ imbalances, can be carried out, for examplefrom continuous frequency pilots.

According to the invention, it is therefore possible to jointly adaptthe estimates of the frequency and clock offsets and the IQ imbalances(imbalances between the in-phase components (or I components) and phasequadrature components (or Q components) of the receiver signal).

A first IQ imbalance estimate can be carried out after a coarsefrequency synchronisation, or after a fine frequency offset correction.

This method can also include a channel estimate step and correction ofthis estimate according to the frequency and clock offsets and the IQimbalances.

Correction of the frequency and clock offsets can be carried out fromthe signal obtained by fast Fourier transform in the receiver, or indeedfrom a channel estimate.

Correction of the frequency and clock offsets can be carried out fromtwo pilots or learning sequences, p₁ and p₂, that are consecutive intime or with interleaved data symbols.

A channel estimate step can be provided, which can be correctedaccording to the IQ imbalance and possibly according to clock and/orfrequency offsets.

The invention also concerns a correction process, in a wirelessreceiver, of a received signal s1, where this signal includes an errordue to a frequency and/or clock offset as well as a gain and/or phaseimbalance, in which:

the received signal s1 is digitised,

the gain and/or phase imbalance of the digitised signal is correctedbefore fast Fourier transformation of the signal.

A step for correction of the error due to a frequency and/or clockoffset, before digitisation of the received signal, or afterdigitisation and before fast Fourier transformation of the signal, canbe provided.

According to a variant, a step for correction of the error due to aclock offset is carried out after fast Fourier transformation of thesignal.

The invention also concerns a receiver device that includes means forcorrection of an IQ imbalance, including:

means for estimating the correction of the IQ imbalance, according toimbalance residual variations since a preceding estimate of the IQimbalance,

means for correction of the IQ imbalance according to this estimate, inorder to obtain a corrected estimate of the IQ imbalance,

means for correction of frequency and clock offsets.

The IQ imbalance estimate can be carried out from pilots or learningsequences, which give rise to transitions due to the opposite IQimbalances.

The IQ imbalance estimate can be carried out from two pilots or learningsequences.

The IQ imbalance estimate can be carried out, for example, from twopilots or learning sequences, p₁ and p₂, p₁ being composed, for example,of a pseudo-random sequence, and p₂ being identical, for example, to p₁in the first half of its samples and opposite to p₁ in the second halfof its samples. With these two pilots, we get transitions due to the IQimbalances which are opposite.

Such a device can also include means to calculate the imbalance residualvariations according to an interference signal of carriers and mirrorsubcarriers, for example, according to a criterion for minimising theenvelope of the interference signal.

The imbalance residual variations can be calculated according to aparameter |E|² that is characteristic of the envelope of saidinterference signal.

Preferably, only the transitions of the interference signal are takeninto account.

A device according to the invention can also include:

means for measuring the value of the complex pilot frequency samples inthe neighbourhood of the transitions,

means for comparing these samples to the samples of the transmittedpilot and for calculating the characteristic parameter |E|² of theenvelope of the IQ imbalances interference.

Means can also correct the βest estimate of the IQ imbalances, inrelation to the preceding estimate, proportionally to$\frac{\partial{E}^{2}}{\partial\beta^{\prime}},$where β′ represents the residual IQ imbalance.

The invention also concerns a receiver device that includes means forcorrection of an IQ imbalance, including:

means for estimating the correction of the IQ imbalance, from pilots orlearning sequences which give rise to transitions due to the opposite IQimbalances,

means for correction of the IQ imbalance according to this estimate, inorder to obtain a corrected estimate of the IQ imbalance,

means for correction of frequency and clock offsets.

The IQ imbalance estimate can be carried out from two pilots or learningsequences.

The IQ imbalance estimate can be carried out from two pilots or learningsequences, p₁ and p₂, with p₁ being composed, for example, of apseudo-random sequence and p₂ being identical, for example, to p₁ in thefirst half of its samples and opposite to p₁ in the second half of itssamples.

A receiver device according to the invention can also include means forcorrection of a signal s2, received and digitised by a wireless receiveraccording to the IQ imbalance.

The correction of the signal s2 can be carried out before a Fouriertransform operation.

The imbalance residual variations can be obtained from the signalobtained by fast Fourier transform (FFT) in the receiver.

In a device according to the invention, means can advantageously be usedto effect a first IQ imbalances estimate either after a coarsesynchronisation, or after a fine frequency correction.

Means for channel estimate and for correction of this estimate accordingto the frequency and clock offsets and of the IQ imbalances, can also beprovided.

Means for correction of frequency and clock offsets can perform thiscorrection from the signal obtained by fast Fourier transform (FFT) inthe receiver or from a channel estimate.

Means for correction of frequency and clock offsets can effect thiscorrection from two pilots or learning sequences, p₁ and p₂, that areconsecutive in time or with interleaved data symbols.

Channel estimate means can also be provided, with channel estimate beingcorrected according to the IQ imbalance and/or according to clock and/orfrequency offsets.

The invention also concerns a computer program that includes theinstructions to implement a method according to the invention.

The invention also concerns a data medium, capable of being read by acomputer system, including data in coded form, to implement a methodaccording to the invention.

The invention also concerns a software product that includes a datamedium suitable to be read by a computer system, and used to implement amethod according to the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B represent the diagram of a digital radio transmissionaccording to prior art,

FIGS. 2A and 2B represent correction processes according to the priorart,

FIG. 3 represents a first embodiment of a method and of a deviceaccording to the invention,

FIG. 4 represents a second embodiment of a method and of a deviceaccording to the invention,

FIGS. 5A to 5C illustrate the effect of the interference of mirrorsubcarriers due to the IQ imbalances,

FIGS. 6A and 6B represent a sequence of steps of processes according tothe invention,

FIGS. 7A-7C are results of comparative simulations, between processesimplementing an algorithm of the invention and according to the priorart,

FIG. 7D represents the results of simulating a method according to theinvention.

FIGS. 8 and 9 represent structures of a system for the broadcasting ofmessages on mobile telephone devices and a diagram of the components ofa mobile telephone device.

DETAILED PRESENTATION OF PARTICULAR EMBODIMENTS

According to the invention, we are aiming to correct residual offsets ina signal.

A symbol and frame synchronisation may have been carried out beforehandfor such a signal, as well as a coarse frequency synchronisation.

The residual frequency offset concerned is less than half of thefrequency separation between subcarriers for example.

The signals concerned are complex and sampled in the time domain (thesesignals are indicated in what follows by variables in lower case) or thefrequency domain (these signals are indicated in what follows byvariables in upper case).

These signals appear at the input and output of the different blocks ofthe reception chains described in FIGS. 3 and 4, each of which concernsone embodiment of the invention.

Each of the blocks described in FIGS. 3 and 4 will be described below.

In these two figures, the two analogue and digital domains are separatedsymbolically by a broken line 101, 201.

An input signal s is assigned, both in frequency and in IQ imbalance,and this is represented symbolically in FIGS. 3 and 4 by means 102, 104,202, and 204.

The incoming signal to the digital part, after digitisation (by meansnot shown in the figures) is applied to means 106 in order to compensatefor the IQ imbalance (FIG. 3) or means 206 for compensation both of theIQ imbalances and of the frequency offsets (FIG. 4).

In FIG. 3, the frequency offsets are compensated upstream, in theanalogue part, while the two corrections take place in the digital partin FIG. 4.

In both cases, the signal s3 produced by means 106 and 206 is subjectedto processing by fast Fourier transform (FFT) by means 108 and 208.

The signal S4 thus produced can be sent to means 110 and 210 for channelestimate.

From signal S4, means 112, 212 are used to effect an IQ imbalancesestimate, with this estimate enabling means 106, 206 to correct thesignal s2 after digitisation, but before FFT processing.

From signal S4, means 114, 214 are used to carry out an estimate of thefrequency and clock offsets, and this estimate enables means 206 (FIG.4) to correct the signal s2 after digitisation, but before FFTprocessing, or means 102 (FIG. 3) to correct the incoming signal, beforedigitisation.

This estimate also allows the IQ imbalance estimate to be refined bymeans 112, 212, as well as, possibly, channel estimate.

In the embodiment of FIG. 4, a clock offset can also be corrected afterFFT by means 209 in order to compensate for clock offsets. In fact theclock offsets are not easy to compensate before FFT. In addition, suchmeans 109 to compensate for clock offsets can also be provided in thediagram of FIG. 3, at the FFT output, as shown in this figure by brokenlines.

Pilot signals 113 and 213 are sent regularly, and these signals enablemeans 112, 212, 114, and 214 to calculate the estimates of the IQimbalances and the frequency and clock offset estimates. These pilotsignals are at known frequencies.

The estimate means 112, 114, 212, 214 effect the correction estimatesfrom the digital signals output from the FFT, or possibly from thesignals coming from means 209 or 109, but also from pilot sequences 113,213.

The correction signals produced by these estimate means are used whereappropriate to correct channel estimate of means 110, 210 for channelestimate.

However the signal produced by these means 110, 210 is in fact not verydamaged in relation to the incoming signal in these means, which isalready a corrected signal.

An output signal 115, 215, and possibly a channel estimate signal, areproduced by the system.

As can be seen in FIGS. 3 and 4, means 110, 210 for channel estimateplay no part in the error estimate calculations.

A frequency offset Δf between the transmitter and receiver creates aphase shift which is expressed according to sampling period ^(T) ^(e) :s ₁(k)=s(k).e ^(j)*^(2π)*^(Δf)*^(k)*^(T) ^(e)

For its part, the IQ disparity is characterised by the two imbalanceparameters, namely gain ε and phase ΔΦ:Re{s ₂}=(1+ε)cos ΔΦRe{s ₁}−(1+ε)sin ΔΦIm{s ₁}Im{s ₂}=(1−ε)cos ΔΦIm{s ₁}−(1−ε)sin ΔΦRe{s ₁}Thens ₂ =α.s ₁ +β.s ₁*Where:α=cos ΔΦ−jε sin ΔΦβ=ε cos ΔΦ−j sin ΔΦ

s2 is the incoming signal in the digital part of the device (see FIGS. 3and 4).

It can be characterised in an equivalent manner in OFDM by theinterferences of the mirror subcarrier. After the Fourier Transformstep:S ₂ =α.S ₁ +β.S ₁ ^(m)*.

In general, S^(m) refers to the mirror signal of any signal S. S^(m) isthe signal in which one has switched subcarriers “n” and subcarriers“N-n”, where N is the number of subcarriers. S* is the conjugate signalof S.

As illustrated in FIGS. 3 and 4, IQ imbalances compensation can becarried out immediately after analogue-digital conversion by means ofthe estimates of the IQ parameters coming from means 112, 212 forestimating the IQ disparity:${s_{3}(k)} = \frac{{\alpha_{est}^{*}{s_{2}(k)}} - {\beta_{est}{s_{2}^{*}(k)}}}{{\alpha_{est}}^{2} - {\beta_{est}}^{2}}$

where s₂ is the damaged signal and s₃ is the corrected signal accordingto estimates α_(est) and β_(est) of parameters α and β of the IQimbalances.

The corrected signal of the IQ imbalances is then given by:${s_{3}(k)} = \frac{{\left( {{\alpha_{est}^{*}\alpha} - {\beta_{est}\beta^{*}}} \right) \cdot {s_{1}(k)}} - {\left( {{\beta_{est}\alpha^{*}} - {\alpha_{est}^{*}\beta}} \right) \cdot {s_{1}(k)}^{*}}}{{\alpha_{est}}^{2} - {\beta_{est}}^{2}}$

If we call α′ and β′ the residual offsets, which indicate the separationbetween the actual values of α and β and their estimated value, then:$\alpha^{\prime} = \frac{{\alpha_{est}^{*}\alpha} - {\beta_{est}\beta^{*}}}{{\alpha_{est}}^{2} - {\beta_{est}}^{2}}$$\beta^{\prime} = \frac{{\beta_{est}\alpha^{*}} - {\alpha_{est}^{*}\beta^{\prime}}}{{\alpha_{est}}^{2} - {\beta_{est}}^{2}}$

and we have:s ₃(k)=α′s ₁(k)+β′s ₁(k)*

The adaptation algorithms are used to minimise β′ and to make α′unitary.

Since these two parameters are related (since α and β are themselvesrelated), it is possible to act upon either, or on a combination of thetwo, in order to compensate for the IQ imbalances.

To simplify the calculations, it is preferable to seek to minimise β.

As already indicated above, the compensation of frequency and clockoffsets is carried out either by sending a control signal to thefrequency synthesis means 102 (as illustrated in FIG. 3), or bycorrecting the frequency offset before the Fast Fourier transform step,and the clock offset after the Fast Fourier transform step (asillustrated in FIG. 4), or in a looped system of the digital PLL type.

It is also possible to coarsely compensate these frequency and clockoffsets in the analogue stages, and to correct the residual offsets inthe digital stages. Digital correction of the frequency offset consistsof a phase rotation:s ₄(k)=s ₃(k).e ^(−j)*^(2π)*^(Δf) ^(est) *^(k)*^(T) ^(e)

where s₃ is the damaged signal and s₄ is the corrected signal accordingto the estimated Δf_(est) of the frequency offset and Te is the samplingperiod. In the architecture of FIG. 3, correction of the frequencyoffset is analogue (s₄=s₃).

The digital correction of the clock offset consists of a phase rotationafter FFT:S ₅(p)=S ₄(p).e ^(−j)*^(2π)*^(p)*^(δt) ^(est) ^(/T) ^(e)

where S₄ is the damaged signal and S₅ is the corrected signal accordingto the estimated δt_(est) of the clock offset.

Steps for calculation and updating of the estimates of IQ imbalanceswill now be presented.

The estimate parameters of the IQ imbalances are determined byestimating a residual variation of the imbalance in relation to apreceding estimate or the preceding estimate.

This estimate can be carried out by virtue of the continuous frequencypilots P(n) a sequence in which all the frequency samples are known), byminimising the envelope of the parasitic signal.

After the Fourier Transform step, the IQ imbalances correspond in factto an interference signal of the mirror subcarriers, as explained belowwith reference to FIGS. 5A-5C.

By way of an example, FIG. 5A represents the modulus of the propagationchannel, which is constant for the pilots of the subcarriers anddecreasing for the pilots of the mirror subcarriers.

FIG. 5B represents pilots p(n) (pilot at subcarrier n) and the mirrorpilots. pm(n) is the mirror pilot at subcarrier N-n.

FIG. 5C represents the interference resulting from the interference ofthe pilots and the mirror pilots. It is to this interference that the IQimbalances correspond. The solid-line curve of FIG. 5C in factrepresents signal S5, at the output of the module to compensate for theclock offset.

Whenever the ratio between pilot on subcarrier “n” and the mirror piloton subcarrier “N-n” changes, interference signal S5 changes its sign.

By observing these “transitions”, it is possible to extract, in thefrequency domain, an estimate of the IQ imbalances.

These are p(n), the value of the pilot on subcarrier “n”, and pm(n), thepilot on the mirror subcarrier “N-n”, where N is the number ofsubcarriers.

A transition is presents when:$\frac{p_{m}\left( {n + 1} \right)}{p\left( {n + 1} \right)} \neq \frac{p_{m}(n)}{p(n)}$

In order to estimate the characteristic parameter β of the IQimbalances:

we measure the value of the complex pilot frequency samples in theneighbourhood of the transitions,

we compare these samples to the samples of the transmitted pilot andfrom these we extract a characteristic parameter of the envelope of theIQ imbalances interferences,

we weight this parameter possibly, in the adaptation algorithm.

The adaptation algorithm can minimise the envelope of the IQ imbalanceinterference by using the following quadratic criterion:${{E(n)}}^{2} = {\frac{\left( {{{S_{5}(n)}{p\left( {n + 1} \right)}} - {{S_{5}\left( {n + 1} \right)}{p(n)}}} \right){p_{m}(n)}}{\left( {{{p\left( {n + 1} \right)}{p_{m}(n)}} - {{p(n)}{p_{m}\left( {n + 1} \right)}}} \right){S_{5}(n)}^{m^{*}}}}^{2}$

It is possible to reduce the effect of channel variation by using thefollowing criterion: ${{E(n)}}^{2} = {\frac{\begin{matrix}{{\left( {{{S_{5}(n)}{p\left( {n + 1} \right)}} - {{S_{5}\left( {n + 1} \right)}{p(n)}}} \right){p_{m}(n)}} -} \\{\left( {{{S_{5}\left( {n + 1} \right)}{p\left( {n + 2} \right)}} - {{S_{5}\left( {n + 2} \right)}{p\left( {n + 1} \right)}}} \right){p_{m}\left( {n + 1} \right)}}\end{matrix}}{\begin{matrix}{{{S_{5}(n)}^{m^{*}}\left( {{{p\left( {n + 1} \right)}{p_{m}(n)}} - {{p(n)}{p_{m}\left( {n + 1} \right)}}} \right)} -} \\{{S_{5\quad m}(n)}^{*}\left( {{{p\left( {n + 2} \right)}{p_{m}\left( {n + 1} \right)}} - {{p\left( {n + 1} \right)}{p_{m}\left( {n + 2} \right)}}} \right)}\end{matrix}}}^{2}$

where S₅(n) is the received signal on subcarrier “n”, S_(5m)(n) is thereceived signal on the mirror subcarrier, p(n) is the value of the piloton subcarrier “n” and p_(m)(n) is the pilot on the mirror subcarrier.

In relation to the known criteria of document WO03/101064, the value ofthe criteria according to the invention, or of the criterion concerningerror minimisation between consecutive subcarriers, will now bedemonstrated.

As can be seen from this document, the estimate parameters of the IQimbalances can be carried out from channel estimate by minimising thequadratic error between consecutive subcarriers. The estimate by themethod of least squares gives the following: β_(est)^(′) = A/B, avec:$A = \begin{pmatrix}{{{\hat{H}}_{p + 1}\frac{2K\quad{\sin\left( \frac{\pi\left( {{\Delta\quad f\quad T} + {\left( {p + 1} \right)\quad\frac{\delta\quad t}{T}}} \right)}{2K} \right)}}{\sin\left( {\pi\left( {{\Delta\quad f\quad T} + {\left( {p + 1} \right)\quad\frac{\delta\quad t}{T}}} \right)} \right)}{\mathbb{e}}^{{- j}\quad*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}{({{\Delta\quad f\quad T} + {{({p + 1})}\quad\frac{\delta\quad t}{T}}})}}} -} \\{{\hat{H}}_{p}\frac{2K\quad{\sin\left( \frac{\pi\left( {{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}} \right)}{2K} \right)}}{\left. {\sin\left( {{{\pi\Delta}\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}} \right)} \right)}{\mathbb{e}}^{{- j}\quad*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}{({{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}})}}}\end{pmatrix}$ $B = \begin{pmatrix}{{t_{p + 1}{\hat{H}}_{p + 1}^{*m}\frac{2K\quad{\sin\left( \frac{\pi\left( {{\Delta\quad f\quad T} + {\left( {p + 1} \right)\quad\frac{\delta\quad t}{T}}} \right)}{2K} \right)}}{\sin\left( {\pi \cdot \left( {{\Delta\quad f\quad T} + {\left( {p + 1} \right)\quad\frac{\delta\quad t}{T}}} \right)} \right)}{\mathbb{e}}^{j\quad*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}{({{\Delta\quad f\quad T} + {{({p + 1})}\quad\frac{\delta\quad t}{T}t}})}}} -} \\{t_{p}{\hat{H}}_{p}^{*m}\frac{2K\quad{\sin\left( \frac{\pi\left( {{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}} \right)}{2K} \right)}}{\sin\left( {\pi\left( {{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}} \right)} \right)}{\mathbb{e}}^{j\quad*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}{({{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}t}})}}}\end{pmatrix}$

where Ĥ is the measurement or the estimate of the channel withoutinter-carrier interference (see its detailed expression later), δt isthe clock offset, and T is the sampling period.

We can make the following simplifying assumptions:$\frac{2K\quad{\sin\left( \frac{\pi\left( {{\Delta\quad f\quad T} + {\left( {p + 1} \right)\quad\frac{\delta\quad t}{T}}} \right)}{2K} \right)}}{\sin\left( {\pi\left( {{\Delta\quad f\quad T} + {\left( {p + 1} \right)\quad\frac{\delta\quad t}{T}}} \right)} \right.} \approx \frac{2K\quad{\sin\left( \frac{\pi\left( {{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}} \right)}{2K} \right)}}{\sin\left( {\pi\left( {{\Delta\quad f\quad T} + {p\quad\frac{\delta\quad t}{T}}} \right)} \right.}$So  that: $\begin{matrix}{\beta_{est}^{\prime} = \frac{\left( {{{\hat{H}}_{p + 1}{\mathbb{e}}^{{- j}\quad*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}{({{\Delta\quad f\quad T} + {{({p + 1})}\quad\frac{\delta\quad t}{T}}})}}} - {{\hat{H}}_{p}{\mathbb{e}}^{{- j}\quad*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}{({{\Delta\quad f\quad{({1 + {\delta\quad t}})}} + {p\quad\delta\quad t}})}}}} \right)}{\left( {{t_{p + 1}{\hat{H}}_{p + 1}^{*m}{\mathbb{e}}^{j\quad*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}{({{\Delta\quad f\quad T} + {{({p + 1})}\quad\frac{\delta\quad t}{T}}})}}} - {t_{p}{\hat{H}}_{p}^{*m}{\mathbb{e}}^{j\quad*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}{({{\Delta\quad f} + {p\quad\delta\quad t}})}}}} \right)^{*}}} \\{= \frac{\left( {{{\hat{H}}_{p + 1}{\mathbb{e}}^{{- j}\quad*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}\frac{\delta\quad t}{T}}} - {\hat{H}}_{p}} \right)}{\left( {{t_{p + 1}{\hat{H}}_{p + 1}^{*m}{\mathbb{e}}^{j\quad*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}\frac{\delta\quad t}{T}}} - {t_{p}{\hat{H}}_{p}^{*m}}} \right)^{*}}}\end{matrix}$

The IQ imbalances estimate is therefore sensitive to the clock andfrequency offsets which rotate the phase from one subcarrier to thenext. There can be a strong influence by these offsets on the IQimbalance estimate, up to 100% of the estimate. In practice one can takethe quadratic mean of the above expression in order to be more robust inrelation to the noise present in the channel and the receiver:$\beta_{est}^{\prime} = \frac{\begin{matrix}{\sum\limits_{p = {- K}}^{K}\left( {{{\hat{H}}_{p + 1}{\mathbb{e}}^{{- j}\quad*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}\frac{\delta\quad t}{T}}} - {\hat{H}}_{p}} \right)} \\\left( {{t_{p + 1}{\hat{H}}_{p + 1}^{*m}{\mathbb{e}}^{j\quad*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}\frac{\delta\quad t}{T}}} - {t_{p}{\hat{H}}_{p}^{*m}}} \right)^{*}\end{matrix}}{\sum\limits_{p = {- K}}^{K}{{{t_{p + 1}{\hat{H}}_{p + 1}^{*m}{\mathbb{e}}^{j\quad*2\quad\pi*\frac{{2\quad K} - 1}{2\quad K}\frac{\delta\quad t}{T}}} - {t_{p}{\hat{H}}_{p}^{*m}}}}^{2}}$

If the channel was previously corrected in respect of the frequency andclock offsets, then the estimates can be written more simply:$\beta_{est}^{\prime} = \frac{\sum\limits_{p = {- K}}^{K}{\left( {{\hat{H}}_{p + 1} - {\hat{H}}_{p}} \right)\left( {{t_{p + 1}{\hat{H}}_{p + 1}^{*m}} - {t_{p}{\hat{H}}_{p}^{*m}}} \right)^{*}}}{\sum\limits_{p = {- K}}^{K}{{{t_{p + 1}{\hat{H}}_{p + 1}^{*m}} - {t_{p}{\hat{H}}_{p}^{*m}}}}^{2}}$

According to the invention, the estimate is adapted iteratively by theuse of β′, which tends toward 0 when the estimate approaches the valuesof the real imbalances. Adaptation can be carried out by a method of thegradient type (Least Mean Square or Recursive Least Square).β_(est)(n+1)=β_(est)(n)+μ.β′.α*≈β_(est)(n)+μ.β′.α_(est)(n)*where μ is a convergence factor.And then:${\alpha_{est}\left( {n + 1} \right)} = {\sqrt{1 - {{Im}\left\{ {\beta_{est}\left( {n + 1} \right)} \right\}^{2}}} - {j\quad\frac{{Re}\left\{ {\beta_{est}\left( {n + 1} \right)} \right\}{Im}\left\{ {\beta_{est}\left( {n + 1} \right)} \right\}}{\sqrt{1 - {{Im}\left\{ {\beta_{est}\left( {n + 1} \right)} \right\}^{2}}}}}}$

The criterion for minimisation of the interference envelope will bedetailed below.

Let p(n) be the value of the pilot sequence at the nth subcarrier,p_(m)(n) the mirror value, s(n) the signal corresponding to this pilotafter FFT, and s_(m)(n) the mirror value.

For two consecutive samples of the same value, and of different mirrorvalues, the separation between these samples corresponds to the width ofthe envelope of the IQ imbalances and to channel variation.

Let: $\begin{matrix}{{E(n)} = {\frac{{{s(n)}{p\left( {n + 1} \right)}} - {{s\left( {n + 1} \right)}{p(n)}}}{{s_{m}(n)}^{*}}\frac{p_{m}(n)}{{{p\left( {n + 1} \right)}{p_{m}(n)}} - {{p(n)}{p_{m}\left( {n + 1} \right)}}}}} & (1)\end{matrix}$

E corresponds to the half envelope of the parasitic signal due to the IQimbalances and to channel variation, the whole being “normalised” by themirror channel. E corresponds in fact to parameter β′.

In fact, if e(n) is the signal that would be received on subcarrier “n”if there was no IQ imbalance,s(n)=α′e(n)+β′e _(m)(n)*

One can then develop the above criterion (1) as follows:${E(n)} = {\frac{\begin{matrix}{\quad{{\alpha^{\quad\prime}\left\lbrack {{{p\left( {n + 1} \right)}\quad{e(n)}} - {{p(n)}\quad{e\left( {n + 1} \right)}}} \right\rbrack}\quad +}\quad} \\{\quad{\beta^{\quad\prime}\left\lbrack {{{p\left( {n + 1} \right)}\quad{\quad{e_{m}(n)}}^{*}} - {{p(n)}\quad\quad{e_{m}\left( {n + 1} \right)}^{*}}} \right\rbrack}}\end{matrix}}{\left( {{{p\left( {n + 1} \right)}{p_{m}(n)}} - {{p(n)}{p_{m}\left( {n + 1} \right)}}} \right)\left\lbrack {{\alpha^{\prime}{e_{m}(n)}^{*}} - {\beta^{\prime}{e(n)}}} \right\rbrack}{p_{m}(n)}}$

The first term [p(n+1)e(n)−p(n)e(n+1)] corresponds to the channelvariation from one subcarrier to another.

Two successive pilot samples are, if one neglects the sign, close to onecarrier or the other. Therefore:${e_{m}\left( {n + 1} \right)}^{*} \approx {\frac{p_{m}\left( {n + 1} \right)}{p_{m}(n)}{{e_{m}(n)}^{*}.}}$

If the channel does not vary much, and with the above approximation, wecan deduce that:${{E(n)} \approx {\frac{\beta^{\prime}\left\lbrack {{{p\left( {n + 1} \right)}{e_{m}(n)}^{*}} - {\frac{{p(n)}{p_{m}\left( {n + 1} \right)}}{p_{m}(n)}{e_{m}(n)}^{*}}} \right\rbrack}{\left( {{{p\left( {n + 1} \right)}{p_{m}(n)}} - {{p(n)}{p_{m}\left( {n + 1} \right)}}} \right){s_{m}(n)}^{*}}{p_{m}(n)}}} = {{\beta^{\prime}\frac{{e_{m}(n)}^{*}}{{s_{m}(n)}^{*}}} \approx \beta^{\prime}}$

If the channel varies in a quasi-linear manner between three successivesamples (a reasonable assumption), the second expression:${E(n)} = \frac{\left( {{\left( {{{s(n)}{p\left( {n + 1} \right)}} - {{s\left( {n + 1} \right)}{p(n)}}} \right){p_{m}(n)}} - {\left( {{{s\left( {n + 1} \right)}{p\left( {n + 2} \right)}} - {{s\left( {n + 2} \right)}{p\left( {n + 1} \right)}}} \right){p_{m}\left( {n + 1} \right)}}} \right)}{\left( {{{s_{m}(n)}^{*}\left( {{{p\left( {n + 1} \right)}{p_{m}(n)}} - {{p(n)}{p_{m}\left( {n + 1} \right)}}} \right)} - {{s_{m}\left( {n + 1} \right)}^{*}\left( {{{p\left( {n + 2} \right)}{p_{m}\left( {n + 1} \right)}} - {{p\left( {n + 1} \right)}{p_{m}\left( {n + 2} \right)}}} \right)}} \right)}$

gives a channel variation term[(p(n+1)e(n)−p(n)e(n+1))−(p(n+2)e(n+1)−p(n+1)e(n+2))] that is smallerthan [p(n+1)e(n)−p(n)e(n+1)] and negligible in estimate β′.

In order to attenuate the bias due to channel variation, then from theabove expression E(n), one can therefore subtract two consecutivevariations.

The adaptation of the estimates (in FIGS. 3 and 4: in estimate block112, 212 of the imbalances), can be carried out by a method of thegradient type (Least Mean Square or Recursive Least Square) whichiteratively minimises the |E|² criterion on all of the subcarriers. Thealgorithm is therefore given by:${\beta_{est} = {\beta_{est} + {\mu\frac{\partial{E}^{2}}{\partial\beta^{\prime}}}}},$where μ is the convergence factor, a formula which indicates theadaptive character of the algorithm. In other words, a previous value ofβest is corrected of the residual variations of the IQ imbalance, theseresidual variations being indicated by the term$\frac{\partial{E}^{2}}{\partial\beta^{\prime}}.$

-   -   αest and βest are also linked by:        $\alpha_{est} = {\sqrt{1 - {{Im}\left\{ \beta_{est} \right\}^{2}}} - {j\frac{{Re}\left\{ \beta_{est} \right\}{Im}\left\{ \beta_{est} \right\}}{\sqrt{1 - {{Im}\left\{ \beta_{est} \right\}^{2}}}}}}$

The choice of μ will depend on what is wanted in terms of precision andspeed of convergence. If the μ factor is chosen to be low, thenprecision is good, but the speed of convergence is low, and vice versaif μ is larger.

The iterative estimate of βest can be carried out as soon as pilots areavailable.

The above developments show that the |E|² estimator is linked directlyto the β′ error on the imbalance parameter β (non-biased estimator).

The interference envelope can also be weighted by channel variation byuse of the simplified criterion:${{E(n)}}^{2} = {\frac{\left( {{{S_{5}(n)}{p\left( {n + 1} \right)}} - {{S_{5}\left( {n + 1} \right)}{p(n)}}} \right)}{\left( {{{p\left( {n + 1} \right)}{p_{m}(n)}} - {{p(n)}{p_{m}\left( {n + 1} \right)}}} \right)}}^{2}$

Also, due to the transition selection points, there is a reduction inthe sensitivity of these expressions to the effects of the frequency,and the estimates are all the better for this.

In fact, only one parameter (β) suffices in order to have theinformation on the gain and phase.

By eliminating the weak subcarriers from the estimate (and therefore oflow signal-to-noise ratio), we get a criterion that is not verysensitive to interference and to noise. This elimination can be achievedby direct measurement of the received subcarrier. And by consideringonly the “transitions” of the interference signal, we render thealgorithm less complex in terms of calculation time.

Another criterion that can be used is minimisation of the error betweenconsecutive subcarriers in channel estimate, developed in document WO03/101064 (IQ-FD), modified in order to be implanted in an adaptivestructure, as explained above in the demonstration. It is more sensitivehowever to the inter-carrier interference generated by the frequency andclock offsets than the previous criterion.

The estimate of frequency and clock offsets can also be carried out fromchannel estimate.

The measurement or the estimate of the channel without inter-carrierinterference is given by: ${{\hat{H}}_{p} = {\begin{pmatrix}{{{\alpha.H_{\quad p}}{\mathbb{e}}^{\quad{j^{*}\quad 2\quad\pi^{*}\quad\frac{{2\quad K}\quad - \quad 1}{\quad{2\quad K}}\quad{({{\Delta\quad{fT}}\quad + \quad{p\quad\frac{\delta\quad t}{\quad T}}})}}}} +} \\{{\beta.\frac{\quad X_{\quad p}^{*m}}{\quad X_{\quad p}}}H_{\quad p}^{*m}{\mathbb{e}}^{{- \quad j^{*}}\quad 2\quad\pi^{*}\quad\frac{{2\quad K}\quad - \quad 1}{\quad{2\quad K}}\quad{({{\Delta\quad{fT}}\quad + \quad{p\quad\frac{\delta\quad t}{\quad T}}})}}}\end{pmatrix}\frac{\sin\quad\left( {\pi\quad\left( {{\Delta\quad{fT}} + {p\frac{\delta\quad t}{\quad T}\quad t}} \right)} \right)}{2K\quad{\sin\left( \frac{\pi\quad\left( {{\Delta\quad{fT}} + {p\frac{\delta\quad t}{\quad T}}} \right)}{2\quad K} \right)}}}}\quad$

The difference between two measurements on two pilots that areconsecutive in time comes from the frequency and clock offsets. If weeffect their correlation, we get:${{{\hat{H}}_{1,p}{\hat{H}}_{2,p}^{*}} = {\begin{pmatrix}{{{{\alpha }.^{2}{H_{p}}^{2}}{\mathbb{e}}^{{- j^{*}}2\pi^{*}\frac{{2K} - 1}{2K}{({{\Delta\quad{fT}} + {2K\frac{\delta\quad t}{T}}})}}} + {{{\beta }^{2}.{\frac{X_{p}^{*m}}{X_{p}}}^{2}}{H_{p}^{*m}}{\mathbb{e}}^{j^{*}2\pi^{*}\frac{{2K} - 1}{2K}{({{\Delta\quad{fT}} + {2K\frac{\delta\quad t}{T}}})}}} +} \\{2{Re}\left\{ {{\alpha.\beta.H_{p}}H_{p}^{*m}\frac{X_{p}^{*m}}{X_{p}}} \right\}{\cos\left( {2\pi\frac{{2\quad K} - 1}{2\quad K}\left( {{\Delta\quad{fT}} + {2K\frac{\delta\quad t}{T}}} \right)} \right)}}\end{pmatrix} \times {\frac{\sin\left( {\pi\left( {{\Delta\quad{fT}} + {p\frac{\delta\quad t}{T}}} \right)} \right)}{2K\quad{\sin\left( \frac{\pi\left( {{\Delta\quad{fT}} + {p\frac{\delta\quad t}{T}}} \right)}{2K} \right)}} \cdot \frac{\sin\left( {\pi\left( {{2\Delta\quad{fT}} + {\left( {p + {2K}} \right)\frac{\delta\quad t}{T}}} \right)} \right)}{2K\quad{\sin\left( \frac{\pi\left( {{2\Delta\quad{fT}} + {\left( {p + {2K}} \right)\frac{\delta\quad t}{T}}} \right)}{2K} \right)}}}}}\quad$

In practice, if pilots and mirror pilots are decorrelated, taking themean of the subcarriers from this expression allows us to rendernegligible the inter-carrier interferences and the effects of the IQimbalances in the estimate of offsets:${\frac{1}{2\pi}{{angle}\left( {E\left\lbrack {{\hat{H}}_{i,p}{\hat{H}}_{2,p}^{*}} \right\rbrack} \right)}} = {{\Delta\quad{fT}} + {2K\frac{\delta\quad t}{T}}}$

Likewise, for a channel estimate between two consecutive subcarriers, wehave:${\frac{1}{2\pi}{{angle}\left( {E\left\lbrack {{\hat{H}}_{p}{\hat{H}}_{p + 1}^{*}} \right\rbrack} \right)}} = \frac{\delta\quad t}{T}$

Once the clock offset has been estimated, the frequency offset can thenbe deduced.

The above calculations of the clock and frequency offsets can be carriedout either on the signals at the FFT output or on the channel estimate.

This estimate of frequency and clock offsets can also be carried outfrom two pilots or learning sequences, p₁ and p₂, that are consecutivein time or spaced with data symbols. In this case, H is replaced in theabove formulae, by the received signal/known signal ratio. We get then:$\frac{\delta\quad t}{T_{e}} = {\frac{1}{2\pi}{{angle}\left( {E\left\lbrack {{S_{5}(p)}{S_{5}^{*}\left( {p + 1} \right)}} \right\rbrack} \right)}}$${N\quad\Delta\quad{fT}_{e}} = {{\frac{1}{2\pi}{{angle}\left( {E\left\lbrack {{S_{5,1}(p)}{p_{1}(p)}^{*}{p_{2}(p)}{S_{5,2}^{*}(p)}} \right\rbrack} \right)}} - {N\frac{\delta\quad t}{T_{e}}}}$If the p₁ and p₂ sequences are identical, then:${{N\quad\Delta\quad{fT}_{e}} = {{\frac{1}{2\pi}{angle}\quad\left( {E\left\lbrack {{S_{5,1}(p)}{S_{5,2}^{*}(p)}} \right\rbrack} \right)} - {N\frac{\delta\quad t}{T_{e}}}}}\quad$

Continuation of frequency offset estimate can be carried out in this waybetween two pilots spaced by “Ns” data symbols. For this, it sufficesthat the normalised frequency offset is less than 0.5/Ns.

With the aid of the various estimates carried out, channel estimate canalso be corrected:

regarding the frequency and clock offsets:${\overset{\sim}{H}}_{p} = {{\hat{H}}_{p}{\mathbb{e}}^{{- j^{*}}2\pi^{*}\frac{N - 1}{N}{({{\Delta\quad{fNT}_{e}} + {p\frac{\delta\quad t}{T_{e}}}})}}\frac{N\quad{\sin\left( \frac{\pi.\left( {{\Delta\quad{fNT}_{e}} + {p\frac{\delta\quad t}{T_{e}}}} \right)}{N} \right)}}{\sin\left( {\pi.\left( {{\Delta\quad{fNT}_{e}} + {p\frac{\delta\quad t}{T_{e}}}} \right)} \right)}}$${{\overset{\sim}{H}}_{p} = {{\hat{H}}_{p}{\mathbb{e}}^{{- j^{*}}2\pi^{*}\frac{N - 1}{N}{({{\Delta\quad{fNT}_{e}} + {p\frac{\delta\quad t}{T_{e}}}})}}}},$for a sufficiently large N,

regarding the IQ imbalances:${\overset{\sim}{\overset{\sim}{H}}}_{p} = {{\frac{{\alpha.^{*}{\overset{\sim}{H}}_{p}} - {{\beta.t_{p}}{\overset{\sim}{H}}_{p}^{*m}}}{{\alpha }^{2} + {\beta }^{2}}{where}\quad{tn}} = \frac{p_{m}(n)}{p(n)}}$

regarding the noise, by calculating the mean over some (2M) consecutivesubcarriers:${\overset{\sim}{\overset{\sim}{\overset{\sim}{H}}}}_{p} = {\frac{1}{2M}{\sum\limits_{k = {p - M}}^{p + M}\quad\frac{{\alpha.^{*}{\overset{\sim}{\overset{\sim}{H}}}_{k}} - {{\beta.t_{p}}{\overset{\sim}{\overset{\sim}{H}}}_{k}^{*m}}}{{\alpha }^{2} + {\beta }^{2}}}}$

Due to the adaptive character of the architecture of the invention, itrapidly becomes unnecessary to correct channel estimate.

In practice, it suffices to effect these channel estimate correctionsonly on the very first channel estimates.

One example of the execution of an adaptation method according to theinvention includes the following steps:

correction or compensation of the frequency offset between transmitterand receiver, from an estimate of this offset obtained previously,

compensation, in the incident signal, of the IQ imbalances, from anestimate of these imbalances obtained previously,

estimate, in the frequency domain, of the residual IQ imbalances from aknown signal,

estimate, in the frequency domain, of the residual frequency and clockoffset between transmitter and receiver,

updating of the characteristic magnitudes of the IQ imbalances and ofthe frequency and clock offset in the correction or compensationsystems.

The chaining of these operations of synchronisation and compensations ofthe imperfections can be carried out according to the diagram of FIG.6A, which is given by way of an example.

step S1: frame and symbol synchronisation,

step S2: coarse synchronisation of the frequency, and adjustment of thelocal oscillator frequency,

step S3: the fast Fourier transform step,

step S4: synchronisation of the clock frequency, and then (S41)continuation of frequency and clock (residues cancellation).

step S5: IQ imbalances estimate, and then (S51) IQ imbalancescorrection,

step S6: channel estimate correction, and then (S61) equalisation.

Some operations in this diagram can be permutated.

One can also extend the joint compensation algorithm for the frequencyand clock offsets and the IQ imbalances to the systems that do noteffect channel estimate.

It is possible to effect the first IQ imbalances estimate after coarsefrequency synchronisation, but it is preferable to do so after a firstfine frequency offset correction, which results in a better signal tointerference and noise ratio.

Estimate adaptation can be carried out at receiver switch-on.

A periodic update allows monitoring of the component variations, sincethese variations are slow in relation to the arrival of the pilots.

The adaptive architecture of the invention effectively and rapidlycompensates the frequency and clock offsets and the IQ imbalancesjointly, and allows channel estimate to be corrected automatically.

Moreover, no transfers to memory are necessary and there is no latencyperiod. Updating of the estimates also require only one pilot sequence.

The simulations show that the IQ imbalances compensation algorithmfunctions for large uncorrected frequency offsets.

Use of the criterion for minimising the envelope of the interferencesignal, in particular renders the adaptation algorithm robust and rapid,even in the presence of a coarse frequency offset. The fact ofconsidering only the “transitions” of the interference signal alsorenders the algorithm less complex and less sensitive to inter-carrierinterference.

The algorithms described in this present invention have been implantedin a MC-CDMA communication chain in SystemC.

Frequency offset and IQ imbalances models greatly damage theperformances of the system. The adaptive architectures of FIGS. 3 and 4are successful in compensating these distorting elements. It is thisthat is illustrated in FIG. 7A, which indicates the binary error rate(BER) according to the signal-to-noise ratio (SNR, in dB) where thechannel used is the “bran E” channel.

The I curve corresponds to the binary error rate without anycompensation.

Curves II, III, IV and V correspond respectively to the followingarchitectures and algorithms:

curve II: the architecture of FIG. 3 and the algorithm provided in WO03/101064,

curve III: the architecture of FIG. 3 and the algorithm of theinvention,

curve IV: the architecture of FIG. 4 and the algorithm given in WO03/101064,

curve V: the architecture of FIG. 4 and the algorithm of the invention.

The results obtained for the architecture of FIG. 3 do not however allowfor the precision faults of the synthesiser.

Table I below brings together the BER data drawn from these curves, at10, 12.5 and 15 kHz. TABLE I Bran E 0.058 0.0049 0.000205 Frequencyoffset = 1 kHz and IQ 0.5 0.5 0.5 imbalance = −(10) dB/0.1 rad (Curve I)Curve II 0.059 0.0049 0.000182 Curve III 0.058 0.0047 0.000208 Curve IV0.062 0.0052 0.00023 Curve V 0.065 0.0053 0.00022

Curves II-V lead one to think that the two algorithms, that of documentWO 03/101064 and that according to the invention, are comparable. Infact, these curves show the effectiveness of the adaptive architecturefor the two algorithms. Also, what these curves do not show is thesuperior rapidity of convergence of the algorithm of the invention,which is reflected in the curves of FIGS. 7B and 7C.

These FIGS. 7B and 7C compare the first estimates of the IQ parametersaccording to the two criteria considered in the presence of anuncompensated frequency offset. It can be seen that the algorithm forminimising the envelope of the interference signal, according to thispresent invention, is less sensitive to the presence of a high frequencyoffset (FIG. 7C) than the algorithm of document WO 03/101064 (FIG. 7B).The fact of considering only the “transitions” of the interferencesignal limits the impact of the inter-carrier interferences (but rendersthe algorithm a bit more sensitive to noise).

It is also possible to use two pilot sequences, chosen in such a mannerthat the transitions due to the IQ imbalances are opposite.

In fact, in order not to overload the frame of a communication bysequences that contain no data, it can be judicious to employ suchpilots, used traditionally for channel estimate and fine frequencysynchronisation, during frequency offset and of IQ imbalances estimate.

This allows us to simplify the complexity of the frequency offset and IQimbalances correction and estimate algorithms, since this has verylittle impact on channel estimate.

For example, it is possible to consider a first pilot composed of apseudo-random sequence, and a second pilot, identical to the first inthe first half of its samples and oppose on its mirror part, such as p₁and p₂ below for example: $p_{1} = \begin{matrix}{\left\lbrack {\underset{\underset{+}{︸}}{1 - 1 - 1 + 1 + 1 - 1 + 1 + 1 + 1}\underset{\underset{+}{︸}}{{- 1} - 1 - 1 + 1 - 1 + 1 + 1 - 1}} \right\rbrack \times} \\\frac{1 + j}{\sqrt{2}}\end{matrix}$ $p_{2} = \begin{matrix}{\left\lbrack {\underset{\underset{+}{︸}}{1 - 1 - 1 + 1 + 1 - 1 + 1 + 1 + 1}\underset{\underset{-}{︸}}{{+ 1} + 1 + 1 - 1 + 1 - 1 - 1 + 1}} \right\rbrack \times} \\\frac{1 + j}{\sqrt{2}}\end{matrix}$

Given that a random sequence after FFT gives a blank Gaussian signal,allowing channel estimate over all the frequencies of the OFDMsubcarriers, these pilots that include pseudo random sequences are verysuitable for the purpose of effecting a channel estimate.

In relation to the previous methods of implementation, the use of theabove pilots enable us in particular to simplify the complexity of theIQ imbalances estimate, frequency offset, and channel estimatealgorithms.

The invention can be implemented with an adaptive structure, such asthat represented in FIG. 3 or FIG. 4. In this case, the adaptive processcarried out is identical to that described previously, where thechaining of these operations for synchronisation and compensation of theimperfections can be carried out according to the diagram of FIG. 6A,which is given by way of an example only.

The use of these pilots also enables us to use a reception chain with anon-adaptive structure. Such a structure differs, for example, fromthose represented in FIGS. 3 and 4 through the fact that the estimatesare not updated in estimate blocks 110, 112, 114, 210, 212 and 214. Inthis case, the operations for synchronisation and compensations of theimperfections can be carried out according to the diagram of FIG. 6B. Inrelation to the diagram of FIG. 6A, block S6 of FIG. 6B does not loop onblock S3 (because the structure is not adaptive).

With such pilots, and if one does not consider the inter-carrierinterferences which behaves like white noise, we get the following atthe output of the FFT step: $S_{5_{1,p}} = \begin{matrix}{\left( {{\alpha.p_{1,p}.H_{p}.{\mathbb{e}}^{j{.2}{\pi.\frac{N - 1}{N}}{({\Delta\quad{f.T}})}}} + {\beta.p_{1,p}^{*m}.H_{p}^{*m}.{\mathbb{e}}^{{- j}{.2}{\pi.\frac{N - 1}{N}}{({\Delta\quad{f.T}})}}}} \right) \cdot} \\\frac{\sin\left( {\pi\left( {\Delta\quad{f.T}} \right)} \right)}{N.{\sin\left( \frac{\left( {{\pi\Delta}\quad{f.T}} \right)}{N} \right)}}\end{matrix}$ $\begin{matrix}{S_{5_{2,p}} = {\left( {{\alpha.p_{2,p}.H_{p}.{\mathbb{e}}^{j{.2}{\pi.\frac{N - 1}{N}}{({\Delta\quad{f.T}})}}} + {\beta.p_{2,p}^{*m}.H_{p}^{*m}.{\mathbb{e}}^{{- j}{.2}{\pi.\frac{N - 1}{N}}{({\Delta\quad{f.T}})}}}} \right) \cdot}} \\\frac{\sin\left( {\pi\left( {\Delta\quad{f.T}} \right)} \right)}{N.{\sin\left( \frac{\pi\left( {\Delta\quad{f.T}} \right)}{N} \right)}}\end{matrix}$

Therefor, for ${0 \leq p < \frac{N}{2}},$p_(1,p)=p_(2,p) and p_(1,p)*^(m)=−p_(2,p)*^(m), we have:$S_{5_{1,p}} = {\begin{pmatrix}{{\alpha \cdot p_{1,p} \cdot H_{p} \cdot {\mathbb{e}}^{{j \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f \cdot T}})}}} +} \\{\beta \cdot p_{1,p}^{\,^{*}m} \cdot H_{p}^{\,^{*}m} \cdot {\mathbb{e}}^{{{- j} \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f \cdot T}})}}}\end{pmatrix} \cdot \frac{\sin\left( {\pi\left( {\Delta\quad{f \cdot T}} \right)} \right)}{N \cdot {\sin\left( \frac{\pi\left( {\Delta\quad{f \cdot T}} \right)}{N} \right)}}}$$S_{5_{2,p}} = {\begin{pmatrix}{{\alpha \cdot p_{1,p} \cdot H_{p} \cdot {\mathbb{e}}^{{j \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f \cdot T}})}}} -} \\{\beta \cdot p_{1,p}^{\,^{*}m} \cdot H_{p}^{\,^{*}m} \cdot {\mathbb{e}}^{{{- j} \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f \cdot T}})}}}\end{pmatrix} \cdot \frac{\sin\left( {\pi\left( {\Delta\quad{f \cdot T}} \right)} \right)}{N \cdot {\sin\left( \frac{\pi\left( {\Delta\quad{f \cdot T}} \right)}{N} \right)}}}$And for${\frac{N}{2} \leq p < N},{p_{1,p} = {{{- p_{2,p}}\quad{and}\quad p_{1,p}^{\,^{*}m}} = p_{2,p}^{\,^{*}m}}},$we have: $S_{5_{1,p}} = {\begin{pmatrix}{{\alpha \cdot p_{1,p} \cdot H_{p} \cdot {\mathbb{e}}^{{j \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f \cdot T}})}}} +} \\{\beta \cdot p_{1,p}^{\,^{*}m} \cdot H_{p}^{\,^{*}m} \cdot {\mathbb{e}}^{{{- j} \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f \cdot T}})}}}\end{pmatrix} \cdot \frac{\sin\left( {\pi\left( {\Delta\quad{f \cdot T}} \right)} \right)}{N \cdot {\sin\left( \frac{\pi\left( {\Delta\quad{f \cdot T}} \right)}{N} \right)}}}$$S_{5_{2,p}} = {\begin{pmatrix}{{{- \alpha} \cdot p_{1,p} \cdot H_{p} \cdot {\mathbb{e}}^{{j \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f \cdot T}})}}} +} \\{\beta \cdot p_{1,p}^{\,^{*}m} \cdot H_{p}^{\,^{*}m} \cdot {\mathbb{e}}^{{{- j} \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f \cdot T}})}}}\end{pmatrix} \cdot \frac{\sin\left( {\pi\left( {\Delta\quad{f \cdot T}} \right)} \right)}{N \cdot {\sin\left( \frac{\pi\left( {\Delta\quad{f \cdot T}} \right)}{N} \right)}}}$

Since it is equally probable that the interferences arising from the IQimbalances is added or subtracted, the estimate algorithm for thefrequency offset is not affected in relation to the previous embodiment.Thus we get:${\Delta\quad{f_{est} \cdot T_{e}}} = {{{\frac{1}{2\quad\pi} \cdot \frac{N}{N - 1} \cdot {E\left\lbrack {{angle}\left( {S_{5_{1,p}}p_{1,p}^{*}p_{2,p}S_{5_{2,p}}^{*}} \right)} \right\rbrack}}\quad{for}\quad 0} \leq p < \frac{N}{2}}$${\Delta\quad{f_{est} \cdot T_{e}}} = {{{\frac{1}{2\quad\pi} \cdot \frac{N}{N - 1} \cdot {E\left\lbrack {{{angle}\left( {S_{5_{1,p}}p_{1,p}^{*}p_{2,p}S_{5_{2,p}}^{*}} \right)} - \pi} \right\rbrack}}\quad{for}\quad\frac{N}{2}} \leq p < N}$

Thus, by averaging the frequency offset estimate on all availablesubcarriers, it is possible to rid oneself of the noise and interferencedue to the IQ imbalances, and we get a more precise value of thefrequency offset.

Then channel estimate can be calculated, dispensing with the errorsgenerated by the IQ imbalances by calculating the mean over the channelestimates obtained for each of the pilots, corrected for the frequencyoffset. We then get: ${{for}\quad 0} \leq p < {\frac{N}{2}\text{:}}$${\hat{H}}_{p} = {\frac{1}{2}\frac{p_{1,p}}{\alpha}{{\mathbb{e}}^{{j \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f \cdot T_{e}}})}}\begin{pmatrix}{{S_{5_{1,p}}\frac{N \cdot {\sin\left( \frac{\pi\left( {\Delta\quad{f_{est} \cdot T_{e}}} \right)}{N} \right)}}{\sin\quad\left( {\pi\left( {\Delta\quad{f \cdot T_{e}}} \right)} \right)}} +} \\{S_{5_{2,p}}\frac{N \cdot {\sin\left( \frac{\pi\left( {2 \times \Delta\quad{f_{est} \cdot T_{e}}} \right)}{N} \right)}}{\sin\quad\left( {\pi\left( {\Delta\quad{f \cdot T_{e}}} \right)} \right)}{\mathbb{e}}^{{j \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f_{est} \cdot T_{e}}})}}}\end{pmatrix}}}$ ${{for}\quad\frac{N}{2}} \leq p < {N\text{:}}$${\hat{H}}_{p} = {\frac{1}{2}\frac{p_{1,p}}{\alpha}{{\mathbb{e}}^{{j \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f \cdot T_{e}}})}}\begin{pmatrix}{{S_{5_{1,p}}\frac{N \cdot {\sin\left( \frac{\pi\left( {\Delta\quad{f_{est} \cdot T_{e}}} \right)}{N} \right)}}{\sin\quad\left( {\pi\left( {\Delta\quad{f_{est} \cdot T_{e}}} \right)} \right)}} -} \\{S_{5_{2,p}}\frac{N \cdot {\sin\left( \frac{\pi\left( {2 \times \Delta\quad{f_{est} \cdot T_{e}}} \right)}{N} \right)}}{\sin\quad\left( {\pi\left( {\Delta\quad{f_{est} \cdot T_{e}}} \right)} \right)}{\mathbb{e}}^{{j \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f_{est} \cdot T}})}}}\end{pmatrix}}}$We then effect an IQ imbalance estimate by evaluating the β parameter inaccordance with the following formulae:${{for}\quad 0} \leq p < {\frac{N}{2}\text{:}}$$\beta_{est} = {\frac{1}{2}\frac{p_{1,p}^{m}}{{\hat{H}}_{p}^{\,^{*}m}}{{\mathbb{e}}^{{j \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f_{est} \cdot T_{e}}})}}\begin{pmatrix}{{S_{5_{1,p}}\frac{N \cdot {\sin\left( \frac{\pi\left( {\Delta\quad{f_{est} \cdot T_{e}}} \right)}{N} \right)}}{\sin\quad\left( {\pi\left( {\Delta\quad{f_{est} \cdot T_{e}}} \right)} \right)}} -} \\{S_{5_{2,p}}\frac{N \cdot {\sin\left( \frac{\pi\left( {2 \times \Delta\quad{f_{est} \cdot T_{e}}} \right)}{N} \right)}}{\sin\quad\left( {\pi\left( {\Delta\quad{f_{est} \cdot T_{e}}} \right)} \right)}{\mathbb{e}}^{{j \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f_{est} \cdot T}})}}}\end{pmatrix}}}$ ${{for}\quad\frac{N}{2}} \leq p < {N\text{:}}$$\beta_{est} = {\frac{1}{2}\frac{p_{1,p}^{m}}{{\hat{H}}_{p}^{\,^{*}m}}{{\mathbb{e}}^{{j \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f \cdot T_{e}}})}}\begin{pmatrix}{{S_{5_{1,p}}\frac{N \cdot {\sin\left( \frac{\pi\left( {\Delta\quad{f_{est} \cdot T_{e}}} \right)}{N} \right)}}{\sin\quad\left( {\pi\left( {\Delta\quad{f_{est} \cdot T_{e}}} \right)} \right)}} +} \\{S_{5_{2,p}}\frac{N \cdot {\sin\left( \frac{\pi\left( {2 \times \Delta\quad{f_{est} \cdot T_{e}}} \right)}{N} \right)}}{\sin\quad\left( {\pi\left( {\Delta\quad{f_{est} \cdot T_{e}}} \right)} \right)}{\mathbb{e}}^{{j \cdot 2}\quad{\pi \cdot \frac{N - 1}{N}}{({\Delta\quad{f_{est} \cdot T}})}}}\end{pmatrix}}}$

This estimate can also be averaged over N subcarriers.

It is also possible to calculate an estimate of α by using the formulathat relates αest and βest:$\alpha_{est} = {\sqrt{1 - {{Im}\left\{ \beta_{est} \right\}^{2}}} - {j\quad\frac{{Re}\left\{ \beta_{est} \right\}{Im}\left\{ \beta_{est} \right\}}{\sqrt{1 - {{Im}\left\{ \beta_{est} \right\}^{2}}}}}}$

The data symbols can therefore be compensated for the IQ imbalancesbefore the FFT step by:${s_{3}(k)} = \frac{{\alpha_{est}^{*}{s_{2}(k)}} - {\beta_{est}{s_{2}^{*}(k)}}}{{\alpha_{est}}^{2} - {\beta_{est}}^{2}}$for the IQ imbalances, and

s₄(k)=s₃(k)e^(−j)*^(2π)*^(Δf) ^(est) *^(k)*^(T) ^(e) for the frequencyoffset

One can therefore jointly and simply correct channel estimate and thedata of the IQ imbalances and frequency offset by:

a frequency offset estimate,

and a channel estimate,

an IQ imbalance estimate,

and a sequential or simultaneous correction of the data symbols beforethe FFT step.

The IQ imbalance estimate algorithm, combined with the use of a firstpilot composed of a pseudo-random sequence, and a second pilot that isidentical to the first in the first half of its samples and opposite onits mirror part, has been tested for an OFDM system with 128subcarriers.

The theoretical data are as follows:Gain imbalance=0.1=>Re(β)=0.0995Phase imbalance=0.1=>Im(β)=−0.0998

The following table represents the sensitivity of the IQ imbalanceestimate in relation to the noise of the propagation channel. Thesimulation is carried out for a propagation channel with selectivefading. Re(β) Im(β) Relative SNR dB estimate estimate error (%) −5 0.081−0.033 49.2 0 0.113 −0.109 11.58 5 0.106 −0.109 7.97 10 0.103 −0.1065.03 15 0.102 −0.104 3.45 20 0.101 −0.102 1.87 25 0.101 −0.101 1.35 300.101 −0.1 1.07

FIG. 7D represents the sensitivity of the IQ imbalances estimate inrelation to the noise of the propagation channel. In this figure, it canbe seen, for example, that for a signal-to-noise ratio of between 10 and20 dB, the relative error is between about 5% and 2%, which shows thequality of the estimate carried out.

The results show that we have a robust solution for the algorithm inrelation to the noise of the channel, whatever the propagation channel.The results obtained after correction, in terms of binary error rate,are also very good, since after estimate and correction we have theresults obtained for a system that is now free of damage.

The invention applies generally to all multi-carrier radio receivers,and in particular in the context of local wireless networks (WLAN802.11, Hiperlan II, of digital radio and video broadcast (DAB, DVB),fourth-generation mobile telephone systems.

As far as this last application is concerned, a mobile device and atransmission system implementing the invention will be described withreference to FIGS. 8 and 9.

The system consists of a mobile telephone system (MTS) 60, composed of anetwork server and a transmission infrastructure, of the radio type forexample, and a system of wireless mobiles or portable receiving devices,mobile telephones 80, 100 for example, associated with the network.

Messages 130, 150 are sent to the portable devices 80, 100, and thelatter are able to re-transmit information 70, 90 in return. Each mobilecommunication appliance offers a structure, as illustrated in FIG. 9,and is equipped with a microprocessor and memory zones.

The assembly includes at least one processor 122, a quantity of RAMmemories 124 (for the storage of data), and ROM memories 126 (for thestorage of program instructions, for example). These various elementsare linked by a bus 128.

A peripheral element, such as a keyboard (indicated by references 81 and101 in FIG. 8), allow a user to enter data, in response to a messagedisplayed on its viewing screen for example.

Other peripheral elements can be used in order to effect the input ofdata, such as a voice-activated control device or a touch-screen forexample.

The data can also be entered by using a combination of peripherals suchas those indicated above by way of an example.

Reference 125 refers to management means for inputs 127 and outputs 129.

Each appliance can also be considered as implementing the functionsdescribed above with reference to FIG. 3, 4, 6A or 6B, or to one of themethods according to the invention as described above.

Data relating to an operating system are stored in a memory zone of eachmobile appliance.

In the case of a mobile telephone, it is also possible to add a SIM card(GSM) or USIM card (UMTS) and means to read this card.

Program data in order to effect correction of the IQ imbalance andfrequency and clock offsets can also be stored in a memory zone of eachmobile appliance.

A mobile device such as devices 81 and 101, has storage means that areused to store data relating to the processing mentioned above, and inparticular the various parameters used in the above formulae.

The calculation of each correction of the RSIB imbalance can be carriedout by each mobile device itself, when it receives pilots. Contrary tothe method described in document WO 03/101064, the method according tothe invention does not require two consecutive sequences, and only onesuch sequence (that is one OFDM symbol) suffices.

In relation to the known techniques and in particular that of documentWO 03/101064, the invention offers the following advantages.

To begin with, it employs either pilots or learning sequences withoutdistinction. It is not necessary to permanently have two long learningsequences.

The invention uses the reception of these known sequences directly afterthe Fourier Transform step, and does not require channel estimate (evenso, there can be a channel estimate if desired).

Also, the architecture of the invention is adaptive.

According to the invention, the preferred IQ imbalances estimatecriterion is based on minimising the envelope of the interferencesignal, and this single IQ imbalances estimate criterion can be usedregardless of the value of the frequency offset, that is more than orless than 15 kHz.

Finally, the channel estimate correction is no longer necessary afterthe first frame.

By choosing pilots in such a manner that the transitions due to the IQimbalances are opposite, it is possible to perform simple and effectivecompensation of the IQ imbalances and frequency offsets. Mosttransmission systems of the OFDM type can incorporate, withoutdifficulty, the algorithms that work with these pilots.

1-55. (canceled)
 56. Method for correction of the IQ imbalance of areceiver, in the presence of a frequency and/or clock offset, in orderto obtain a corrected estimate of the IQ imbalance, including: an IQimbalance estimate, according to imbalance residual variations since apreceding estimate of the IQ imbalance, a correction of the frequencyand/or clock offsets and of the IQ imbalance according to the estimateof the imbalance, in order to obtain a corrected estimate of the IQimbalance.
 57. Method according to claim 56, the IQ imbalance estimatebeing carried out from pilots or learning sequences, which give rise totransitions due to the IQ imbalances which are opposite.
 58. Methodaccording to claim 56, the IQ imbalance estimate being carried out fromtwo pilots or learning sequences.
 59. Method according to claim 56, theIQ imbalance estimate being carried out from two pilots or learningsequences, p₁ and p₂, p₁ being composed of a pseudo-random sequence andp₂ being identical to p₁ in the first half of its samples and oppositeto p₁ in the second half of its samples.
 60. Method according to claim56, the imbalance residual variations being calculated according to aninterference signal of carriers and mirror subcarriers.
 61. Methodaccording to claim 60, the residual variations of the imbalance beingcalculated according to a criterion for minimising the envelope of theinterference signal.
 62. Method according to claim 60, the imbalanceresidual variations being calculated according to a characteristicparameter |E|² of the envelope of said interference signal.
 63. Methodaccording to claim 62, only the transitions of the interference signalbeing taken into account.
 64. Method according to claim 63, in which: wemeasure the value of the pilot complex frequency samples in theneighbourhood of the transitions, we compare these samples to thesamples of the transmitted pilot and from these we extract thecharacteristic parameter |E|² of the envelope of the IQ imbalancesinterferences.
 65. Method according to claim 62, the parameter |E|²being equal or proportional to:${{E(n)}}^{2} = {\frac{\left( {{{S_{5}(n)}{p\left( {n + 1} \right)}} - {{S_{5}\left( {n + 1} \right)}{p(n)}}} \right){p_{m}(n)}}{\left( {{{p\left( {n + 1} \right)}{p_{m}(n)}} - {{p(n)}{p_{m}\left( {n + 1} \right)}}} \right){S_{5}(n)}^{m^{*}}}}^{2}$where S₅(n) is the received signal on subcarrier “n”, S_(5m)(n) is thereceived signal on the mirror subcarrier, p(n) is the value of the piloton subcarrier “n” and p_(m)(n) is the pilot on the mirror subcarrier.66. Method according to claim 62, the parameter |E|² being equal orproportional to: ${{E(n)}}^{2} = {\frac{\begin{matrix}{{\left( {{{S_{5}(n)}{p\left( {n + 1} \right)}} - {{S_{5}\left( {n + 1} \right)}{p(n)}}} \right){p_{m}(n)}} -} \\{\left( {{{S_{5}\left( {n + 1} \right)}{p\left( {n + 2} \right)}} - {{S_{5}\left( {n + 2} \right)}{p\left( {n + 1} \right)}}} \right){p_{m}\left( {n + 1} \right)}}\end{matrix}}{\begin{matrix}{{{S_{5}(n)}^{m^{*}}\left( {{{p\left( {n + 1} \right)}{p_{m}(n)}} - {{p(n)}{p_{m}\left( {n + 1} \right)}}} \right)} -} \\{{S_{5m}\left( {n + 1} \right)}^{*}\left( {{{p\left( {n + 2} \right)}{p_{m}\left( {n + 1} \right)}} - {{p\left( {n + 1} \right)}{p_{m}\left( {n + 2} \right)}}} \right)}\end{matrix}}}^{2}$ where S₅(n) is the received signal on thesubcarrier “n”, S_(5m)(n) is the received signal on the mirrorsubcarrier, p(n) is the value of the pilot on subcarrier “n” andp_(m)(n) is the pilot on the mirror subcarrier.
 67. Method according toclaim 62, the βest estimate of the IQ imbalances being corrected, inrelation to the preceding estimate, proportionally to$\frac{\partial{E}^{2}}{\partial\beta^{\prime}},$ where β′ representsthe residual IQ imbalance.
 68. Method according to claim 56, theimbalance residual variations being obtained from the signal S4 obtainedby fast Fourier transform in the receiver.
 69. Method for correction ofthe IQ imbalance of a receiver, in the presence of a frequency and/orclock offset, in order to obtain a corrected estimate of the IQimbalance, including: an IQ imbalance estimate carried out from pilotsor learning sequences, which give rise to transitions due to the IQimbalances which are opposite, a correction of the frequency and/orclock offsets and of the IQ imbalance according to the estimate of theimbalance, in order to obtain a corrected estimate of the IQ imbalance.70. Method according to claim 69, the IQ imbalance estimate beingcarried out from two pilots or learning sequences.
 71. Method accordingto claim 69, the IQ imbalance estimate being carried out from two pilotsor learning sequences, p₁ and p₂, with p₁ being composed of apseudo-random sequence and p₂ being identical to p₁ in the first half ofits samples and opposite to p₁ in the second half of its samples. 72.Method for correction of a signal s2 received and digitised by awireless receiver, including a method for correction of the IQ imbalanceaccording to claim 56, and a correction of the signal S2 according tothis imbalance.
 73. Method according to claim 72, the correction of thesignal s2 being carried out before a Fourier transform operation. 74.Method according to claim 56, a first IQ imbalances estimate beingcarried out after a coarse frequency synchronisation.
 75. Methodaccording to claim 56, a first IQ imbalances estimate being carried outafter a fine frequency offset correction.
 76. Method according to claim56, also comprising a step of channel estimate and correction of thisestimate according to the frequency and clock offsets and of the IQimbalances.
 77. Method according to claim 56, a correction of thefrequency and clock offsets being carried out from the signal S4obtained by Fast Fourier Transform in the receiver.
 78. Method accordingto claim 56, the correction of the frequency and clock offsets beingcarried out from a channel estimate.
 79. Method according to claim 56,the correction of the frequency and clock offsets being carried out fromtwo pilots or learning sequences, p₁ and p₂, that are consecutive intime or with interleaved data symbols.
 80. Method according to claim 56,also comprising a channel estimate step.
 81. Method according to claim80, channel estimate being corrected according to the IQ imbalance. 82.Method according to claim 80, channel estimate being corrected accordingto clock and/or frequency offsets.
 83. A receiver device that includesmeans for correction of an IQ imbalance, comprising: means forestimating IQ imbalance, according to imbalance residual variationssince a preceding estimate of the IQ imbalance, means for correctingfrequency and clock offsets and IQ imbalance, according to the IQimbalance estimate, in order to obtain a corrected estimate of the IQimbalance.
 84. Device according to claim 83, the IQ imbalance estimatebeing carried out from pilots, or learning sequences, which give rise totransitions due to the opposite IQ imbalances.
 85. Device according toclaim 83, the IQ imbalance estimate being carried out from two pilots,or learning sequences.
 86. Device according to claim 83, the IQimbalance estimate being carried out from two pilots or learningsequences, p₁ and p₂, p₁ being composed, for example, of a pseudo-randomsequence and p₂ being identical, for example, to p₁ in the first half ofits samples and opposite to p₁ in the second half of its samples. 87.Device according to claim 83, the imbalance residual variations beingcalculated according to an interference signal of carriers and mirrorsubcarriers.
 88. Device according to claim 83, the residual variationsof the imbalance being calculated according to a criterion forminimising the envelope of the interference signal.
 89. Device accordingto claim 87, the imbalance residual variations being calculatedaccording to a characteristic parameter |E|² of the envelope of theinterference signal.
 90. Device according to claim 89, only thetransitions of the interference signal being taken into account. 91.Device according to claim 90, including: means for measuring the valueof the pilot frequency complex samples in the neighbourhood of thetransitions, means for comparing these samples to the samples of thetransmitted pilot and for calculating the characteristic parameter |E|²of the envelope of the IQ imbalance interference.
 92. Device accordingto claim 89, the βest estimate of the IQ imbalances being corrected, inrelation to the preceding estimate, proportionally to$\frac{\partial{E}^{2}}{\partial\beta^{\prime}},$ where β′ representsthe residual IQ imbalance.
 93. Device according to claim 83, theimbalance residual variations being obtained from the signal obtained byfast Fourier transform in the receiver.
 94. Receiver device comprisingmeans for correction of an IQ imbalance, including: means for estimatingIQ imbalance, from pilots or learning sequences which give rise totransitions due to the opposite IQ imbalances, means for correcting thefrequency and clock offsets and the IQ imbalance, according to the IQimbalance estimate, in order to obtain a corrected estimate of the IQimbalance.
 95. Device according to claim 94, the IQ imbalance estimatebeing carried out from two pilots or learning sequences.
 96. Deviceaccording to claim 94, the IQ imbalance estimate being carried out fromtwo pilots or learning sequences, p₁ and p₂, with p₁ being composed, forexample, of a pseudo-random sequence and p₂ being identical, forexample, to p₁ in the first half of its samples and opposite to p₁ inthe second half of its samples.
 97. Receiver device according to claim89, including means for the correction of a signal s2, received anddigitised by a wireless receiver according to the IQ imbalance. 98.Device according to claim 97, the correction of the signal s2 beingcarried out before a Fourier transform operation.
 99. Device accordingto claim 83, a first IQ imbalances estimate being carried out after acoarse frequency synchronisation.
 100. Device according to claim 83, afirst IQ imbalances estimate being carried out after a fine frequencyoffset correction.
 101. Device according to claim 83, including meansfor estimating a channel and correcting this estimate according to thefrequency and clock offsets and of the IQ imbalances.
 102. Deviceaccording to claim 83, the correction of the frequency and clock offsetsbeing carried out from the signal S4 obtained by fast Fourier transformin the receiver.
 103. Device according to claim 83, the correction ofthe frequency and clock offsets being carried out from a channelestimate.
 104. Device according to claim 83, the correction of thefrequency and clock offsets being carried out from two pilots orlearning sequences, p₁ and p₂, that are consecutive in time or withinterleaved data symbols.
 105. Device according to claim 83, alsoincluding channel estimate means.
 106. Device according to claim 105,channel estimate being corrected according to the IQ imbalance. 107.Device according to claim 105, channel estimate being correctedaccording to clock and/or frequency offsets.
 108. Computer programcomprising instructions to implement a method according to claim 56.109. Data medium, capable of being read by a computer system, comprisingdata in coded form, to implement a method according to claim
 56. 110.Software product comprising a data medium suitable to be read by acomputer system, and used to implement a method according to claim 56.